Analog multipliers, i.e. circuits that takes two analog input signals and produce an output signal proportional to the product of the input signals, are frequently used in analog signal processing.
In particular, analog multipliers or mixers are widely used in modern communication systems in order to realize frequency conversion or translation of modulated signals.
The mixers can be classified as passive and active. Active mixers employ switching transistor pairs for current commutation, such as the so-called Gilbert cell.
A typical Gilbert cell mixer comprises a differential transconductance stage, used to convert an input Radio-Frequency (RF) voltage signal (the RF modulated signal to be converted) into a differential current signal. The differential current signal is fed to two pairs of current switches or switching pairs (quad), which are cross-coupled to one another and are controlled by a voltage signal generated by a local oscillator, so as to perform a current commutation. A differential current signal generated by the two switching pairs can be fed to a load, e.g. a purely resistive load, so as to produce an output voltage.
Active mixers are particularly attractive, and are frequently used in telecommunication applications, because they offer advantages over passive mixers, such as high conversion gain and good port-to port isolation.
In particular, active mixers fabricated in MOS or CMOS technology are desirable, because they can be easily integrated in a semiconductor chip together with other analog or logic circuits.
High linearity, i.e. low intermodulation distortion, and low noise are important features in a mixer, because they greatly affect the dynamic range of most communication systems.
If properly sized, the MOSFETs used in the input stage of an active mixer demonstrate fairly good linearity. The distortion of the two switching pairs is more complex to analyze and depends both on the speed of the switching pairs and on parasitic capacitances (both linear and non linear) at the nodes where the differential current signal generated by the transconductance stage is fed to the two switching pairs (the common source nodes of the switching pairs).
A problem in active mixers, especially those realized in MOS or CMOS technology, is however represented by flicker or 1/f noise. It is known that the main source of this kind of noise are the MOSFETs in the two switching pairs.
In a MOS- or CMOS-technology Gilbert cell mixer, a trade-off between noise and linearity performances exists. The main limitations to high linearity and low noise come from the switching pairs. In fact, for the transconductance stage, the trade-off can be broken at the price of a higher power consumption.
The flicker noise contribution of the switching stage could be reduced using low biasing currents and large area MOSFETs. Unfortunately, this would increase the parasitic capacitances and reduce the switching speed. The results would be a degraded linearity. This effect is due to the non-linear partition of the signal current between the switching MOSFETs and the parasitic capacitances at the common source nodes of the switching pairs.
Thus, flicker noise reduction and increase of linearity have conflicting requirements: while low biasing currents and large MOSFETs are required to reduce the flicker noise, high biasing currents and small parasitic capacitances are required to enhance linearity.
The linearity problem is worsened by the high common-mode signal at twice the frequency of the signal generated by the local oscillator present at the common source nodes of the switching pairs; such common-mode signal originates from the rectification of the large signal produced by the local oscillator. This is particularly true for switching pairs in MOS- or CMOS-technology.
In D. Manstretta et al., “A 0.18 μm CMOS Direct Conversion Receiver Front-END for UMTS”, ISSCC 2002, Session 14, Cellular RF Wireless, Paper 14.6, a solution to overcome this effect has been suggested, consisting of a common-mode LC filter resonating at twice the frequency of the local oscillator signal. In particular, the common-mode LC filter includes two capacitors and one inductor; each capacitor has a first plate connected to the common source node of a respective switching pair, and a second plate connected to a first terminal of the inductor; the second terminal of the inductor is connected to ground.
Thanks to the provision of the common-mode LC filter, the oscillation amplitude of the common source nodes of the switching pairs is greatly reduced, by virtue of the low impedance shown by the filter at twice the frequency of the local oscillator signal. The result is a considerable improvement in linearity.
A drawback of this solution is that as far as the differential radio-frequency signal is concerned, the filter behaves as a capacitor connected between the common source nodes of the quad, and thus worsens the flicker noise performance of the mixer.